Abstract

Using the analytical model we developed for an nth-order cascaded Raman laser, we find the design rules for such lasers. We determine analytical expressions for the cavity length and the output-coupler reflectivity that maximize the output power and minimize threshold power. Simple expressions are obtained in the depleted-pump approximation. Deviations from these expressions when the pump is not completely depleted are shown to be different depending on the parity of the number n of Stokes shifts (cascades). The design rules show that the mirror reflectivity is a critical factor in the laser quality and that the ultimate slope efficiency η is found to be gn/g0. We also find a condition to determine if P-doped fibers are more useful than Ge-doped fibers in Raman fiber lasers based only on the Raman shift and absorption of the fibers.

© 2005 Optical Society of America

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References

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  1. R. W. Boyd, "Stimulated Raman scattering and stimulated Rayleigh-Wing scattering," in Nonlinear Optics (Academic, 1992), pp. 365-388.
  2. R. H. Stolen, J. P. Gordon, W. J. Thomlinson, and H. A. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Am. B 6, 1159-1165 (1989).
    [CrossRef]
  3. M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
    [CrossRef]
  4. S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
    [CrossRef]
  5. M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Electron. 36, 1117-1122 (2000).
    [CrossRef]
  6. G. Vareille, O. Audouin, and E. Desurvire, "Numerical optimisation of power conversion efficiency in 1480 nm multi-Stokes Raman fibre lasers," Electron. Lett. 34, 675-676 (1998).
    [CrossRef]
  7. B. Burgoyne, N. Godbout, S. Lacroix, "Solution of nth-order, cascaded, continuous-wave, Raman fiber lasers. I. Analytical model," J. Opt. Soc. Am. B 22, 764-771 (2005).
    [CrossRef]
  8. E. M. Dianov, "Advances in Raman fibers," J. Lightwave Technol. 20, 1457-1462 (2002).
    [CrossRef]
  9. E. Saulnier, N. Godbout, and S. Lacroix, "Simultaneous measurement of spontaneous and stimulated Raman scattering in optical fibers, in Photonics North 2004: Optical Components and Devices , S. Fafard, ed., Proc. SPIE 5577 , 196-203 (2004).
    [CrossRef]

2005 (1)

2004 (1)

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

2002 (1)

2001 (1)

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

2000 (1)

M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Electron. 36, 1117-1122 (2000).
[CrossRef]

1998 (1)

G. Vareille, O. Audouin, and E. Desurvire, "Numerical optimisation of power conversion efficiency in 1480 nm multi-Stokes Raman fibre lasers," Electron. Lett. 34, 675-676 (1998).
[CrossRef]

1989 (1)

Audouin, O.

G. Vareille, O. Audouin, and E. Desurvire, "Numerical optimisation of power conversion efficiency in 1480 nm multi-Stokes Raman fibre lasers," Electron. Lett. 34, 675-676 (1998).
[CrossRef]

Bouteiller, J. C.

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Burgoyne, B.

Chia, L. C.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

Christiani, I.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

Cristiani, I.

M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Electron. 36, 1117-1122 (2000).
[CrossRef]

Degiorgio, V.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Electron. 36, 1117-1122 (2000).
[CrossRef]

Desurvire, E.

G. Vareille, O. Audouin, and E. Desurvire, "Numerical optimisation of power conversion efficiency in 1480 nm multi-Stokes Raman fibre lasers," Electron. Lett. 34, 675-676 (1998).
[CrossRef]

Dianov, E. M.

Eggleton, B. J.

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Feder, K.

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Godbout, N.

Gordon, J. P.

Haus, H. A.

Headley, C.

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Horn, C.

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Lacroix, S.

Lee, L. W.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

Lim, H. C.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

Mermelstein, M. D.

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Rini, M.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Electron. 36, 1117-1122 (2000).
[CrossRef]

Sim, S. K.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

Steinwurzel, P.

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

Stolen, R. H.

Thomlinson, W. J.

Vareille, G.

G. Vareille, O. Audouin, and E. Desurvire, "Numerical optimisation of power conversion efficiency in 1480 nm multi-Stokes Raman fibre lasers," Electron. Lett. 34, 675-676 (1998).
[CrossRef]

Wu, R. F.

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

Electron. Lett. (2)

S. K. Sim, H. C. Lim, L. W. Lee, L. C. Chia, R. F. Wu, I. Christiani, M. Rini, and V. Degiorgio, "High-power cascaded fibre Raman laser using phosphosilicate fiber," Electron. Lett. 12, 738-739 (2004).
[CrossRef]

G. Vareille, O. Audouin, and E. Desurvire, "Numerical optimisation of power conversion efficiency in 1480 nm multi-Stokes Raman fibre lasers," Electron. Lett. 34, 675-676 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Rini, I. Cristiani, and V. Degiorgio, "Numerical modeling and optimization of cascaded CW Raman fiber lasers," IEEE J. Quantum Electron. 36, 1117-1122 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. D. Mermelstein, C. Headley, J. C. Bouteiller, P. Steinwurzel, C. Horn, K. Feder, and B. J. Eggleton, "Configurable three-wavelength Raman fiber laser for Raman amplification and dynamic gain flattening," IEEE Photon. Technol. Lett. 13, 1286-1288 (2001).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Other (2)

R. W. Boyd, "Stimulated Raman scattering and stimulated Rayleigh-Wing scattering," in Nonlinear Optics (Academic, 1992), pp. 365-388.

E. Saulnier, N. Godbout, and S. Lacroix, "Simultaneous measurement of spontaneous and stimulated Raman scattering in optical fibers, in Photonics North 2004: Optical Components and Devices , S. Fafard, ed., Proc. SPIE 5577 , 196-203 (2004).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Diagram of an nth-order cascaded Raman fiber laser. λj is the wavelength of the jth Stokes wave. Only the output coupler (OC) is not highly reflective. The vertical lines represent the Bragg gratings used as reflectors with reflectivities Rj±.

Fig. 2
Fig. 2

Output power (in dBm) plotted against the cavity length and the output-coupler reflectivity as calculated from Eq. (1). Parameters used for calculation are given in Table 2 of Ref. 7. The left column shows the output power calculated under the depleted–pump approximation. The top row represents the n even case while the bottom row represents the n odd case. The open circle is the optimal cavity length and OC reflectivity obtained by using analytical expressions of Eqs. (11) and (12) in the depleted-pump approximation.

Fig. 3
Fig. 3

Residual pump power in dBm plotted against cavity length and output-coupler reflectivity in the n odd case. The residual pump power diminishes rapidly when the cavity length and–or OC reflectivity are–is increased.

Tables (1)

Tables Icon

Table 1 Parameter Limit Values, n Even Case

Equations (26)

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Pout=-ln(Rn+Rn-)1+Rn+Rn- (1-Rn-)(1-Rn+)×Pinfp4g0Lj=2jevennρj+α02g0-j=1joddn-1ρj,
Pthres=4g0Lj=2jevennρj+α02g0j=1joddn-1ρj 1fp,
η=-ln(Rn+Rn-)1+Rn+Rn- (1-Rn-)(1-Rn+)fp4g0Lj=2jevennρj+α02g0,
fp=1-R0+ exp-4g0Lj=2jevennρj+α02g0,
ρj=αj2gj-ln(Rj-Rj+)4gjL;
Pout=-ln(Rn+Rn-)1+Rn+Rn- (1-Rn-)(1-Rn+)×Pin-Pr4g0L-j=1joddnρj-j=2jevenn-1ρj-α02g0,
Pthres=4g0Li=1ioddnρji=2ievenn-1ρj+α02g0+Pr(Pthres),
η=-ln(Rn+Rn-)1+Rn+Rn- (1-Rn-)(1-Rn+)1-dPrdPin4g0Lj=1joddnρj
Pr=PinR0+ exp-4g0Lj=2jevennρj+α02g0;
Pr=PinR0+ exp-Pin-Prj=1joddnρj.
Lopt,even=(BeBo/AeAo)1/2,
Rn,opt,even+=1Rn- exp-4gnBeAo1/2Pin4g01/2-AeBo-Ao-Be,
ζ=-ln(Rn-Rn+)4gn,Ae=j=0jevenn αj2gj,Ao=j=1joddn-1 αj2gj,
Be=-j=2jevenn-2 ln(Rj-Rj+)4gj,Bo=-j=1joddn-1 ln(Rj-Rj+)4gj.
Lopt,even-n-2n+21/2 ln(R)α¯-0.23n-2n+21/2 RdBα˜.
Rn,opt+1R exp-2 ln(R)1-2n g¯Pinα¯ln(R)-n24-1-n2+1.
R2,opt+=1Rn- exp-4gnAo PinAe4g0Bo1/2-Ae.
Lthres,even=[(BeBo+ζ)/AeAo]1/2.
Pout*=-ln(Rn+)Ping04AeL-ln(Rn+)gn-Ao,
Pthres*=g0Ao4AeL-ln(Rn+)gn,
η*=1g0 1gn-4AeLln(Rn+)-1.
Pout,opt=4gn[(Pin/4g0)1/2-(AeBo)1/2-(AoBe)1/2]2.
Pout,optPPout,optGe.
(AeBo)1/2+(AoBe)P1/2(AeBo)1/2+(AoBe)Ge1/2.
Fαj=0jevenn α3jg3j j=1joddn-1 1g3j1/2+Fαj=1joddn-1 α3jg3j j=2jevenn-2 1g3j1/2j=0jeven3n αjgj j=1jodd3n-1 1gj1/2+j=1jodd3n-1 αjgj j=2jeven3n-2 1gj1/2,
Fα=αPαGe7.6.

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